Excellent point. However, Picard is going by memory and may be off but being a historian I doubt by much if at all.
There is a large gap between the NX and the Constitution and I think Drexler's refit is a perfect fill in. The nx refit could also be a test bed for incorporating Tellarite, Andorian, and Vulcan technology into Starfleet design whereas the Constitution becomes the integrated and mature cruiser.
I think a tale about integrating UFP species and navies into Starfleet would make a great story as well as a reflection of modern social issues.